The OPGG provides a challenging environment for cooperation. The three-way interaction between cooperators, defectors and loners produce natural cyclical dynamics, where cooperative environments favour defection, which in turn makes opting out more advantageous, which in turn leads to the return of cooperation [1]}, [2]}. Similar challenges are faced introducing the possibility of agents punishing one another based on their past actions. In this case the cyclical dynamics involve both the presence of pro-social (punishment of defectors and loners) and of anti-social punishment (punishment of cooperators), with each strategy punishing its would-be invader [3]}. In either case, the average cooperation level resulting from the cyclical behaviour is low.
